Question

For a normal distribution with a mean of μ = 150 and an SD of σ = 15:

3. Find these probabilities: a. p (X > 150)

b. p(X < 120)
c. p(X < 170)
d. p(130 < X < 175)

Answer 1

We are given the distribution here as:

a) The probability here is computed as:

P(X > 150) = 0.5 as for normal distribution, the distribution is symmetric about the mean.

Therefore 0.5 is the required probability here.

b) P(X < 120)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.0228 is the required probability here.

c) P(X < 170)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.9088 is the required probability here.

d) The probability here is computed as:

P(130 < X < 175)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.8610 is the required probability here.